Stellar equilibrium is a balance model. Name both sides: inward gravitation and outward pressure from fusion energy.

Gravity acts inward and tends to collapse a star.

Fusion in the core produces radiation and thermal energy.

Radiation pressure and gas pressure act outward.

In a stable main-sequence star, inward gravitational effects balance outward pressure.

The equilibrium is self-regulating: if fusion increases, expansion cools the core and fusion slows; if fusion decreases, contraction heats the core and fusion increases.

Match each stellar-equilibrium cue to its role.

Match

Reasons

0/5

Describe stellar equilibrium in a main-sequence star.

Saying forces are absent in equilibrium.

Describe stellar equilibrium in a main-sequence star.

Choose

Fusion in stars is a nuclear binding-energy process. It is not chemical burning. The products are more tightly bound, and the mass difference is released as energy.

Fusion combines light nuclei to form heavier nuclei.

In main-sequence stars like the Sun, hydrogen nuclei ultimately form helium-4 through the proton-proton chain.

A simplified outcome is four protons forming one helium-4 nucleus plus positrons, neutrinos, gamma radiation, and energy.

Energy is released because the helium nucleus has greater binding energy per nucleon than the separate protons.

The mass defect is converted to energy according to E=mc².

Match each stellar-fusion cue to the correct idea.

Match

Reasons

0/5

Describe fusion as the source of energy in main-sequence stars.

Calling stellar fusion chemical burning.

Describe fusion as the source of energy in main-sequence stars.

Choose

Fusion conditions are about overcoming the Coulomb barrier. Temperature supplies kinetic energy; density supplies collision rate; the strong force acts only once nuclei are extremely close.

Positively charged nuclei repel each other electrically.

Very high temperature gives nuclei large kinetic energies.

High density or pressure increases the chance of collisions.

Nuclei must get close enough for the strong nuclear force to act attractively.

In stellar cores, temperatures of order 10^7 K and high pressure make fusion possible.

Match each fusion-condition cue to its purpose.

Match

Reasons

0/5

Explain the conditions required for fusion in stars.

Saying high pressure fuses nuclei without mentioning electric repulsion.

Explain the conditions required for fusion in stars.

Choose

Stellar mass is the driver of stellar evolution. Bigger fuel supply does not automatically mean longer life, because massive stars burn fuel far faster.

A star’s initial mass strongly affects its core temperature and pressure.

More massive main-sequence stars have faster fusion rates and greater luminosities.

Because they consume fuel faster, high-mass stars have shorter main-sequence lifetimes.

Lower-mass stars burn fuel more slowly and remain on the main sequence longer.

As stars evolve, their temperature, luminosity, and radius change, so their positions on the HR diagram change.

Match each mass-evolution cue to its effect.

Match

Reasons

0/5

Describe the effect of stellar mass on the evolution of a star.

Saying more massive stars live longer because they contain more fuel.

Describe the effect of stellar mass on the evolution of a star.

Choose

HR diagrams are easy to misread because temperature increases leftward. Always check axes before interpreting region or radius.

The HR diagram plots luminosity on the vertical axis, increasing upward.

Surface temperature is on the horizontal axis and increases to the left.

The main sequence runs diagonally from hot, luminous stars at upper left to cool, dim stars at lower right.

Red giants and supergiants are high luminosity but relatively cool, so they lie toward the upper right.

White dwarfs are hot but low luminosity, so they lie toward the lower left.

Lines of constant radius run diagonally because L = 4πR²σT⁴; larger radius gives greater luminosity at the same temperature.

Label the HR diagram regions and axis trap.

Label

Labels

5

Sketch and interpret an HR diagram.

Putting hot stars on the right because temperature is treated as increasing normally.

Sketch and interpret an HR diagram.

Choose

Parallax is a geometry method. The baseline is Earth’s orbit, but p in the formula is half the total shift. Use arcseconds and parsecs together.

Stellar parallax is the apparent shift of a nearby star against distant background stars as Earth orbits the Sun.

The parallax angle p is half the total angular shift between observations six months apart.

If p is measured in arcseconds, distance in parsecs is d = 1/p.

One parsec is the distance at which 1 AU subtends an angle of 1 arcsecond.

1 pc is about 3.26 light years or 3.09 × 10^16 m.

Parallax becomes less reliable for distant stars because p becomes very small.

Assemble the parallax distance relation.

Formula

Target formula d = 1/p

d

distance to star

pc

p

parallax angle

arcseconds

AU

Earth-Sun distance baseline unit

m

pc

parsec

m or ly

1Identify parallax angle as half the total angular shift.p = half total shift

2Use p in arcseconds.d(pc) = 1/p(arcsec)

3Define parsec.1 pc: 1 AU subtends 1 arcsecond

4State limitation.large distance -> tiny p -> less reliable

Build the formula

Use stellar parallax to calculate distance and define the parsec.

Using the total observed angular shift instead of the parallax angle.

Use stellar parallax to calculate distance and define the parsec.

Choose

This card groups the main stellar measurement tools. Wien gives temperature from peak wavelength; Stefan-Boltzmann gives radius from luminosity and temperature; absorption lines give composition.

A star’s surface temperature can be estimated from its spectrum using Wien’s displacement law: λ_max T = 2.90 × 10^-3 m K.

Hotter stars have shorter peak wavelengths; cooler stars have longer peak wavelengths.

Luminosity, radius, and surface temperature are related by L = 4πR²σT⁴.

Once L and T are known, radius can be calculated from R = sqrt(L/(4πσT⁴)).

A star’s cooler outer atmosphere absorbs specific wavelengths, producing dark absorption lines.

Comparing the absorption-line pattern with laboratory spectra identifies chemical composition.

Assemble the E.5 stellar measurement tools.

Formula

Target formula L = 4πR²σT⁴

L

stellar luminosity

W

R

stellar radius

m

σ

Stefan-Boltzmann constant

W m^-2 K^-4

T

surface temperature

K

λ_max

peak wavelength

m

1Use peak wavelength to find temperature.λ_max T = 2.90×10^-3 m K

2Use Stefan-Boltzmann luminosity relation.L = 4πR²σT⁴

3Rearrange for radius.R = sqrt(L/(4πσT⁴))

4Use absorption-line patterns separately.match dark lines to laboratory spectra

Build the formula

Explain how stellar temperature, radius, and chemical composition can be determined from observations.

Using the same spectral feature for all properties.

Explain how stellar temperature, radius, and chemical composition can be determined from observations.

Choose

E.5 is an observation-rich topic. Keep the physical model of stars connected to the measurement tools: HR diagrams, parallax, spectra, and luminosity.

Fusion in main-sequence stars converts hydrogen into helium and releases energy from mass defect and greater binding energy per nucleon.

Stellar equilibrium balances inward gravity with outward radiation and gas pressure.

Stellar mass controls fusion rate, luminosity, lifetime, and evolution.

The HR diagram plots luminosity upward and surface temperature increasing to the left, with main sequence, giants, supergiants, white dwarfs, instability strip, and constant-radius lines.

Parallax gives distance using d(pc)=1/p(arcsec) for nearby stars.

Wien’s law gives surface temperature, Stefan-Boltzmann gives radius, and absorption spectra reveal chemical composition.

Match each E.5 cue to the model or observation it retrieves.

Match

Reasons

0/8

Summarize the E.5 fusion and stars model.

Listing equations without linking them to observations.

Summarize the E.5 fusion and stars model.

Choose

IB Physics SL E.5 Fusion and stars Notes

Read Stellar equilibrium

Read Fusion in stars

Read Fusion conditions

Read Stellar mass and evolution

Read HR diagram regions

Read Stellar parallax

Read Stellar temperature, radii and spectra

Retrieve the E.5 Fusion and stars Model